The goal of this project is to develop a computer-aided system to detect abnormalities in breasts, cancer particularly, using electrical impedance tomography (EIT) measurements. The present project aims to develop alternative and inexpensive screening tools to assist in diagnosis in situations where mammography is inconclusive. We hypothesize that different abnormalities have different electromagnetic properties and therefore these properties may be identified and classified using electrical impedance data. Although various breast imaging techniques are available, our goal is to statistically detect a deviation from normality. Therefore, our project aims to not only obtain an image of the breast, but to provide a probabilistic assessment of the fact that in the region of interest, the electromagnetic properties of the breast differ from the rest of the tissue or from bilaterally symmetric locations in the contralateral breast. Our project will leverage the effort and activity from a recently funded program project on alternative breast imaging modalities. Specifically we will use, EIT patient data, including cancer data from this project. Three methods will be explored for statistical breast abnormality detection and discrimination: (1) a Breast Signature Pyramid derived directly from the Neumann-to-Dirichlet map, (2) abnormality localization and detection using the Product--Image by reducing the underlying Laplace partial differential equations into a set of coupled ordinary differential equations, (3) the Mixed Model approach to image reconstruction in which optimal regularization parameters will be estimated from the EIT data. These novel approaches are based on recent mathematical discoveries related to the magic Toeplitz matrix, imageless reconstruction of the electromagnetic properties of in vivo tissues using surface measurements, the generalized form of Ohm's law, and a mixed model approach to solving complex inverse problems. PUBLIC HEALTH RELEVANCE The goal of this project is to develop a computer-aided system to detect abnormalities in breasts, cancer particularly, using electrical impedance tomography (EIT) measurements. The proposed project aims to develop alternative and inexpensive screening tools to assist in diagnosis in situations where mammography is inconclusive. We anticipate that our methodology will improve the sensitivity of cancer detection especially for younger women with dense breast tissue.